An investigation into the effect of propeller hull interaction on the structures of the wake field

3 SEI. 1984

ARCHÎEr

f,,,--K E L-PAPER 4/1 - SESSION i

(i-)

&-/

(i.

_1it

')ì'

SYMPOSIUM ON

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

HOVIK OUTSIDE OSLO, MARCH 20. 25., 1977

"AN INVESTIGATION INTO THE EFFECT OF PROPELLER HULL INTERACTION ON THE STRUCTURES OF THE

WAKE FIELD"

By

M. Hoekstra, Netherlands Ship Model Basin, Wageningen, The Netherlands

SPONSOR: DET NORSKE VERITAS

lab. V.

Scheepsbou"

1echnsche

Hog eschao

ABSTRACT

This per deals with the detérminàtion of the effective wake of

a tanker model. The influence of the propeller action on the flow

around the stern of the model was simulated by a diffuser, in order to measure the propeller-hull interaction effects in the propeller plane. Effective wake fields were, derived from thé

flow measurements 'in the orifice of three diffusers, representing

a propeller at various loads. Differences between nominal and effective wake are discussed. Some examples are shown of the

improvement in the correlation of calculated and measured shàft

force and moment fluctuations, which can be 'achieved by using 'an

effective instead of a nominal wake field as input for the

1. INTRODUCTION

Ïn the past years, several calculation methods have been developed

at ship researáh institutes o determine the various aspects of the behaviour of a propeller in the .wake f a ship. The propeller

efficiency, thrust and torque, the extent of cavitation on the

- blades1 the induced pressure fluctuations and the induced unsteady

shaft force and moment can now be calculated more or less

success-fully

The aim.of the dévelopment of these calculation methods is manifold. Théy allow predictions of the propeller behaviour to be made in. an early stage of the design work.Moreover, they are suitable to

study scale effects, while systèmatc parametervariations are

- easily appliéd.

For a fruitful employment ofthese calculation procedures it is nècesarj - that they have a fair accuracy. They should at least give

quali-tatively valuable results. Unfortunately, this requirement is not always met. Especially for the heavily loaded própeliers of f ull-formed Ships, the calculations often lead to unsatisfactory results.

Undoubtedly this is partly duç to hortcomings of the theories underlying the various calculation methods. TBUt probably a more

important cause.of failure is the insufficient knowledge of the mf low to the propeller. Al]. calculations which concern the

- propeller need thé flow field in which the propeller is operating asinput. Until now,. the f:low field measured behind a ship model

withöutprópeller, the socalled nominal wake fièld, has mostly

2

been usedfor this purpose. In general, however, the nominal wake

field is not thé flow field which is actually experienced by the

propeller. The latter is called the effective wake field and can be defined as the flow field behind a shlpwith propeller after

subtraction of the propeller-induced velocities. The differences between nominal and effective wake are due to propeller-hull

interaction effects, which become naturally more pronounced with increasing propeller load and decreasing distance between hull and

propeller. One of these effects is the influence f the. propeller

action on the development of the boundary layer alòng thé hull.

Although we can speculate a good deal on the nature of interaótion

effécts on the wà.ke, we do not know how they really turn out. Let

us therefore consider how they may be measured. First of all, it shouldbe realized that the effeótive wake field is not a real flow

field because the propeller-induoed velocitiès are not contained in it.Effective wake is only af,ictious concept. Inherently, it .s essentially

unmeasurable. To derive its main features we must rely either

upon purely theoretical means (boundary layer calculatjons) br upon a combination of experimental and theoretical means, i.e. measuring some real flow field and modifying it subsequently on

à theoreticál base. With the present abilities to calculate complex viscous flows, the latter approach is for the time being themost

promising Then the most attractive way to derive the effective wake pattern seems to measure the flow field closely ahead of the propeller and to sUbtract the calculated propeller-induced

vélocities. However, when a 5-holes Pitot tube is used as the

-3-.

made too far ahead of the propeller.. Therefore a different

approach was used for the investigations reported in this paper. The propeller was replaced by a conical tube with circular cross-.

section: a diffuser. Such a diffuser, when fitted behind the towed ship model, simulates the flow-sucking action of the propeller. Against the drawbàck of the simulation being not completely correct

- (actuator disk representation), the use of a diffuser has the advantage that velocity measurements can be made in the propeller plane with the standard Pitot apparatus. Of course, the measured flow field contains the diffuser-induced velocities. Recalling that. the velocities induced by the propeller or its substitute do not belong to the effective wake field, the diffuser-induced velocities have to be calculated.

In this paper, the principles of the diffuser test method will be describèd in detail. Moreover, results will be shown of the

derived effective wake fields at various propeller loads and

a comparison with the nomïnal wake field will be made.Soue.illustrations of the improvement of the correlation of calculated and measured

shaft force and moment fluctuations when using effective instead

of nominal wake fiels.are also included.

2. PRINCIPLES OF THE DIFFUSER TEST

A diffuser ma7 bé conceived as a rolled-up hydrofoil-at-incidence.

When it is towed. at constant speed through a fluid at rest, a flow circulation is established which causes the velocity in the.

4

The streamline pattéx'ns produced by a diffuser and an actuator

i rspectively are compared in Fig.i. As shown by this figure,

a diffuser is equivalent to an actuator disk as far as the flow upstream of its orifice is concerned. Since the flow downstream

of the propeller plane is irreievan' in the, present investigation

of propeller-hull interaction effects, the diffuser is with the restrictions of' the actuator disk representation - a proper sub-stitute for thé propeller.

During a diffuser test, the diffuser is fitted to the ship model

such that the örif icé is 'located in the propeller plane and the

diffuser axis coincides with the propeller axis. The experimental

- 2

ee up is shoín in Fig.2. While thé ship model is towed at' constant

speéd, the flow field in the diffuser orif Icé is measured analogous to á standard nominâl 'wake measurement. Thus the inflow to the

diffuser (actuator disk), including effects of diffuser-hull intéraction, is obtained.. By subtracting the diffuser-induced

velocities, thé effective wake field assoòiated with a diffuser c

ctüator, disk), i.è. the approximate effec'tivewake field of the aòtuál propéller, is' obtained. Henceforth, this approximate ef'fective

wake field Will simply be called the èffectve wake field.

'As follóws from what is mentioned above, thé effective wake field can be' dèived from the measured flow field as ,soon as the diffuser

iñduction at thé orifice is known. These diffuser-induced velocities can bé calculated when the diffuser surface is repesented by a

vortex sheet. 'The' local vortex strength of' this sheet is, 'uniquely

determined when the correct mf low conditions are known by requiring impermeability of the sheet, d 'the fulfIllment of the Kutta

condition àtt1e sheet's trailing edge However, these calculations are rather curnBèsome and the inflow is actually unknown, for that is just what we are looking for: the effective flow field.

There-fore a simplification is introduced, that is,, it is assumed that - for our purposes the induction of the diffuser operating in

distorted flow may well be approximated by the induction of the diffuser operating in uniform flow. The latter induction is readily

-

calcul4ted for given diffusèr dimensions (see the Appendix) As a result we obta-iri the induction in the form

=Uf(r)

)

(2.1)

ÙR= Ug(r),

J

where t1A = the axial component of the induced velocity

UR

the radiaI component of the induced velocity

= the velocity .of the uniform onset flow

f and g are calculated functions öf the radius r.

Û can beassumed to be equal to the mean effective axial velocity

= VAe (2.2)

where V is the local effective axial veioity , the overbar

Ae

denotes a volumetric mean value and the effective wake fraction.

In that casé we can make use of the relation

=VAd

(2.3)

stating that the mass f löw through the diffuser orifice equals

where by

R.

¡ di f(r)rdr/Rd o

-6-WAd is the axial cotnponent of the velocity measured in the

- orifIce) ... tisinq (2.1) we can rewrite (2.3) as

U (2.4)

Rdj being the radius of the active area of the diffuser. Since VM.

is measured and f(r) is known from calculations, (2.4) fixes the

vâlüe' of U. The effective velocity field is.then' given by

(r,4)-Uf(r),

(2.5)

VT(It4) = vTd(r,c),. (2.6)

= yçrl4)Ug(r).

-. _{For the purpose of relating the action of a given diffuser to that}

of 'the simulatedpropeller, we'can introdúcea fictitious thrust, equ1 to the thrust of: añ actuator disk which produces the same

upstream flow induction as' the diffuser. This thrust 'is, according

to moméntum theöry, related to the indúced velOcities at the orifce.

2TTRdI

T

'f

J

VAd.2u. rdrd4,

(2.7)

00

in which T'= thrust;'

p'='mass density of water,

r ='radial coordinate, ' '

= angular coordinate,

7

Substituting (2.1) ii (2.7) we find

27rR.

T 2

uf J'1Ad(r,

f(r) rdrd, (2.8)

which provides us with the value of the simulated thrust.

The above analysis of the diffuser test results

is basedon the

assumption expressed by (2.2 One can avoid this

ssumption by

assuming instead the Interaction force of the propeller-hull and the diffusér-hull coitbinations respectively to be equal. How in

this case the. analysis proçeèds will be explained with the aid

3 óf Fig.3. In this figure the balance of forces on a single-screw ship model duriig a propulsion test and adiffuser test are

compared. During a pröpulsion test the sum of the towIng force F1

and the. propeller thrust T exactly compensate the sum of the model resistance R and the propeller-hull interaction force.

AR1 (AR1/T

is. the thrust deduction fractión). So

T+

= R + AR1..

(2.9)

During a. diffuser test, an interaction forcé is also present but no thrust is delivered. Therefore the towing force F2 .häs to

compensate the sum of the model resistance R, the interaction force

AR2 and the resistance of the diffusèr.Rd: .

R +AR2 + Rd.

(2.10)

When the diffUser simulates a thrust T, we ássume the interaction

force AR to be the same as for a propeller delivering a thrust T. Thus, equating AR1, and AR2, we find

Dividing by T yields t and consequently

-8-T+ F1 - R = F2 - R - (2.11) F T+F1-R _{F2_R_Rd} T

T-(2. 1.2) (2 . 13) t

The forces F2 and Rd can easily be measured during the diffuser

test.. When thé thrust.dedUCtiOfl fraction t arid the resistande R aré known f roirt resistance and propulsion testi, the simúlated

-

thrúst T can be càlculate. 'Once T is known, U can be solVed from

(2.8) and the effective velocity f:ield follows from (2.6).

-

In practice the first method of analysis based' on the assumption

(2.2) -is primarily used. Nevertheless, the forces F2 and Rd ae

always measúred during a diffuser test to be able to apply (2.13)

-3. RESULTS AND DISCUSSION

The diffuser test was appliedto 12 in model of a tanker with

a bulbous stern. Three diffusers were used with lengthes of 940, 1340 and 1740 mm respectively. Their geometry is shown in Fig.4. By varying the length of the diffusers at constant diffuser angle., a variation of the simulated propeller loading was obtained.

Hence, the results of the tests should give us an impressipn of the influence of propeller loading, on the wake. The non4nal wake field was also measured for the purpose of çomparison. A five-holes Pitòt tube was used as the velöcity measuring device.

The axial velocity distributions in the nominal wake and in the

three effective wake fields are compared in Fig. 5, whereas the transverse velocity compOnents are shown in Fig.6. "rhe effective

wake fields have been marked with a Cm value This thrust coefficient

CT is defined as

CT

-in which T is the simulated thrus

Becaùse bilge vortices play a dominant role in the following

discussion of Figs. 5 and 6, ït is recalled here that bilge vortex

formation is related to a three-diménsional type of flow separation (see Ref.1). As a consequence of this separation, a vortex sheet

is developed which is convected downstream and rolls up at the

same time (Fig.7). This roll-up causes a local concentratiçn of vorticity which is commonly called the bilge, vortex. What seems to be the approximate location of the separated vortex. layer

10

-in the propeller plané has been -indicated -in Fig.6.

In the nòminal wake field the vortex sheet has a cönsiderable extension. Its rolled-up end is located very near thé edge of the

propeller disk. Experience has learned that at the location of the cèntre of the bilge vortex a high wake region occurs in a nöminal

wake field. This is probably due to the decelerating flow in which

the vortex is developïn'g. The present nominal wake field provides a striking example.

Turning to the effective wake fields, it appears from Fig.6

that the s'hape of thè vortex sheet gradually changeswith increasing

-

propeller lOad. At CT = 2.8 a slight shift of the votèx sheet

towards the propeller axis is noticeable. However, more important is the downward: shift of the upper end of the sheet, i.e. the position

of the bilge vOrtex, an interactiOn effect which ha ben repdrted earlier by Dyne (Ref.2). At the same time the magnitude Of the transverse velocity components has increased. When the propeller load is increased to CT 4.9 the vortex sheet moves primarily in

radiál directiontowards the propeller axis; the downward movement of the bilge vortex does not continue. The strength of the vortex

increases further which cañ be concludèd from the augmentation of. the transvérse velocity components. increasing the, propeller load to CT = 6.0 leads only tO minor additional changes in the vOrtex

Of course the axial velocity distribution of the effective wake fields (Fig.5) shows changes whiçh aredirectly related to the modified vortex flow. The high wake regions associated with the bilge vortex sheêt move' with the sheet. However, the magnitude

of the wake peak at the centre of the, vortex decreases with increasing propeller load and finally ¿linost disappears. Besides, the wake

peak in the 12 o'clock position is, at least at the outer radii, smoother in the effective wake fields than in the nominal wake

field.

As a result of the alterations due to pröpeiler-hull interaction, not only the veiöcity distribution in the effective wake fields is cônsidérably different from the nominal velocity distribution, alsó the wake fraction has decreased substantially. This can be reàdily concludéd from the harmonic analyses of the nominal and

efféctive velocity fields, given in Table 1.

In summary we can distinguish the. following features as the most pronounced propeller-hull interaction effects for the subject

vessel. (i) The bilge vortex changés its position.

Itdoes not

only shift radiälly tOwards the propeller axis ut also downwards. (ii). The strength of the bilge vortex increases whIch leads to high tangèntial velocities. (iii). The wake peak associated with

thè centreof the bilge vortex disappears. (iv). The wake fraction

decreases.

When the cavitation properties or, the dynamic behaviour of a propeller in a wake are to be determined from model tests, the

-

proper simulation of the f low experienced by the full-scale

12

-propeller is a matter of great concern. In this respecta.

- comparisoñ of the results iri.Figs. 5 and 6 with results of wake

scale effect studies (Ref.3) indicates that due observance of

intéraction effects on the wàke is at least as important as taking into account scalé effects.

We shall conclude, this section by showing some examples of the improved correlation of measurèd and calculated shaft forces and moments, achieved by sing diffuser test. results instead of

nominal wake fields. These examples, shown in Fig.8, were adopted from previous diffuser tet applications on' an LNG carriér and a tanker respectively.' The shaft force and mOment components were

calculated wit-ha method based on unsteady linearized lifting

surface theory (Ref.2).An improvement of the correlation is

evident, although some discrepancies still remain. Especially the static transverse force ïs poorly predicted. We should bear

in mind, however, that it is also the component which 'is' hardest to measure accurately.

-. 13

-4. CONCLUDING REMARKS

In this paper a study was made of the effècts. of propeller-hull interaction on the wake field, i.e effecive wake fields were

determined. The basis of this study was a new test method, the

diffuser test. During this test, the propeller action is simulated by à diffuser to allow' the effects f propeller-hull 'interaction

on the wake to be measured in the propeller plane. Due to the simplified representatin of the propeller the diffuser test

cannot and does not pretend to be the final answer to the problem

of'dete'rmining an effective wake field. Nevertheless, the 'test

method provides us with' abetter insight into the flow field actually

experienäed by.a propeller. Its results can'be used successfully

to imprOve the cOrrelatiOn between the calculated and measured

-

behaviour of à propeller ir a wake. ' '

The most significant interaction effects on the wake distribution

of the subject vessel appeared to be a non-radialshift of the bilge

vortex, an ináre'ase f' the bilge vortex strength, a reduction or disappearance of the wake peak associated with the bilge vortex ad a decrease of 'the wake fraction. As a consequence the effective

wake dstribution was found to be remarkably different from the

nominal wake distribution. It can b state'd that the difference between nominal and effective wake is at least as significant as the difference between the nominal wakes of model and' ship

- 14

REFERENCES

HOEKSTRA, M., Prediction of Full-Scale Wake Characteristics Based on Model Wake Sürvey, Paper presented at: the Symposium

on "High powered propulsioñ of large ships", Wageningen,Holland.

See also: International Shipbuilding Progress,

Vol.

22, No 250, June 1975.

DYNE, G., À Study of the Scale Ef fect. on Wake,Propeller Cavitation

and Vibratory Pressure at Hull of Two Tanker M deis,. Transactions

of SÑÀME, November1974.

YOKÒO, K., Measurement of Full-scale Wake Characteristics and their Predictión frOm Model Results - State of the Art, Paper

presented at the Symposium on "High Powered Propulsion of Large

Ships", Wageningen, Hollañd, December 1974..

GENTj W. van, Unsteady Lifting-SurfaCe Theory for Ship Scréws: Dérivation andNiimeriCal Treatment of IntegralEquation,

APPENDIX

Consider anaxisymmetriCal vortex sheet of a finite length in a

uniform, axially-dirécted flow with velocity U0(see Fig. A-1).

Let the vortex sheet be impermeable. Then the vorticity distribution on the sheçt is uniquely determined by the zero-normal-velocity

condition at the sheet and the Kutta condition at the trailing edge

Put wôr (w is thé vorticity and 6r ié the infiniteSimal thickness

of the sheet) equal to r. On base of symmetry considerations it is easily shown that r is constant in circumferential direction.

r is thus a function of x only. The velocity induced by the

above-defined vortex sheet is given in vector form by

úx) =

15

-1

f.

x

A

whére x is the position vectOr of the point where u is calculated,

is the position vector of the point where the integrand is evaluated, =

-x,

sIsI

and dA is ari elemnt of the surfaäe A

of the vOrtex sheet. Iñ the Cartesian do-ordinate system x-y-z, the vector is given by

= I(x-x')±j(r cos4-r'cos')+k(r sinP-r'sin') (Ä.2)

and i by

(A.1)

(-rsinq)+k(rcos').

(A.3)

Hence, the axial and radia. compOnents of x? are respectively

(sxr)A [(r cos4-r' cosq')cos'+(r sinrd sint1')sinct'1 (A.4)

- 16

-Expressing speeds and r as a fraction òf the onset velocity U0 and lengths as a fraction of some representative radius R, the non-dimensional axial and radial components of the induced velocity are given by

b 271 = - ' o'

fx')(x-x)r' cos(-')

¿

r

'4r

_cosG)-r1r'

4rr' 2 (x-x) +(r+r 71/2 1

!

(1-k2 cos2)3/2..dc1 1-k2 2

dxd', (A.6)

dx'd4', (A.7)

where i, x,

X',

r and r' are now dimensionless quantities.

The lading edgé of the vortex sheet is in these formulas located at x=a and the trailing èdge at x=b.

The expressions for and _UR can be further evaluated as follows.

Introducing

(A. 8)

e = -q,

(A.9)

the axial velocity component can be written as

b 211 2

f

r4x'r'

Zr cos (0/2)-r-r'

1

_{[(xx)2(+rt)213I2! [1_k2tos2e/2]3/2}

0(A.1O)

The theory of elliptic integrals yields

in whidh K and E are complete elliptic integrals of. the first

and second kind respectively, which.are known in polynomial form

(Ref.A_1). Using .(A.11) and (A.12) in (A.10) gives

¶/2 2

f

cosa.

J 2

2 3/2

(1-k COS o

In a similar wày we find for u

i

I

í.(x.r'

. F K K-E .1 E

1x_2+(rni)213'2L

1-k2 (i_k)k2j (r+r

1k

i

f

f.(xxt)r

R

-.

[3/2

{2

_[lk2

- 17 -r. r. K.4k)

-

1-k2 (1-k2)k2

2

,213/2

- cosP.')

+(r+r.)

J K-E (1-k2)k2 (A. 12) E 2 dx. 1-k J (A. 13) .(A.14)

Thé integral xpresslons (A.13) a.nd (A.14) are singular if (x,r,)= (x',r','). This singularity is handled properly (seq Ref. A..2) when x and x' are tràrisfòrmed into

½(b-a)-cos ) (A.15)

x'=

(b-a)-cos (A..16)

and the following discretization is applied:

K K-E

2r.

. --...-.-. + i-k2 (1-k2)k2

-(r.+r)

. =i ...-,N . . . . (A:.17) 1-k .1 N- i = Ai lT =0

N-1

=z

j =0 E k2 18 -r.

[(cos.-cos2+r+r

2 Ax' J (2i-1)IT i 2N i:!L

jN

5 ½ for j=0 1. 1 for j>0

rN=o (.Kuttä condition)

3/2

1=1, (A.18)

(A.19)

r. can now be solved iteratively as follows. With initial values

for

_URi;

r.

is determined from (A.18). Substituting these r

values in (A.17) yields UAj. The impermeability condition

-URi/UAi = ()

(A.23)

then provides new values for URi, etc. This iteration, process is

continued until a sufficient aòcurary is obtained. Once the distribution of r is known, the axial and radialcomponents of

the induced veclocity can be determined in àny field point with

19

-REFERENCES

A-l. ABRPMOWITZ, M. and S!EGUN., l.A. : Handbook of Mathematical

Functons, Dover Publictions., New York, 1965.

A-2. WEISSINGER, J. and MAASS1 D.: Theory of the Ducted Propeller. A Review, 7th Symposium on Naval Hydrodynamics, Rome,

Effective wake field 940 ¡mn diffuser 0.333 0.600 0.733 0.867

0.93

A0 0.329 0.357 0.34.5 0.360 . 0.436 0.491 A.1 -0.115 -0.084 -0.015 Ò.040 0.12.7.

O.i8

A2 -0.061 -0.b33 0.002 0.03.6 0.055 0.051 A3 . 0.019 -0.016 -0.045 -0.077 -0.082 -0.089 A4 0.006 0.007 0.005 .0.020 . 0.028 0.035 A5 0.024 0.0.12 0.009 0.005 0.006 . .0.009 A6 0.021

-0O05

. 0.012 0.012 0.006 0.002 À7 Q.007 0.005 0.011 0.017 0.01.1 0.010 0.333 0.467 0.600 0.733 0.867 A0. . 0.368 . 0,381 0.374 0.436 0.564 A1 -0.132 . -0.094 -0.088 -0.033

0103

A2 -0.088 -0.034 0.01.7 Ó.049 s 0.055 A3 0.020 0.001 0.003 -0.029 -0.042 -0.001 -0.027 -0.040 -0.037 -0.032 A5 0.042 0.015 0.020 0.034 0.Ö38 A6. 0.034 -0.003 -0.009 0.003 0.0I6 A7 0.015 -0.003 0.009 0.030 0.013

-20-TABLE 1

Harmonic anâlysis of wake fields (V

= A0+

?ACOS

iq)

- 2

-TABLE 1 (çfljflued); Effective wake field 1340 m diffuser

Effective wake field. 1740 mm diffuser

0.333 0.467 0.600. 0.733 0.867 A0 0.363 0.378 0.404 0.6i3 0.767 A1 -0.i32 -0.109 -0.098 0.054 0.087 A2 -0.042 0.001 -0.014 -0.020

-0045

A3 0.014 -0.005 -0.026 -0.027 -0.018 A4 -0.005 -0.002 -0.010 0.005 0.003 A5 .0.018 0.017 0,020 0.032 0.024 'A6' 0.015 -0.001 0.001 -0.012 -0.010 A7 . . 0.017 0.002 0.006 0.012 .0.010

0.33.30.467

o.60Q

'0M3

'0.867 A0 0.394 0.423 0.48 0.646

0.79

A1 -0.017 -Ò.005 -0.01.9 0.094 0.136 'A2 0.04'7 O.'O2O 0.003 0.003 0.012 A3 0.009 0.005 -O.O02 -.0.017 -0.010 A4 0.015. -0.012 0.Q19 -0.007 -0.012 A5 ' 0.027 0.020 0.015 p.020 :o..ou. A6 ' 0.007 .0.00.6 -0.013 -0.008 '-0.009' A7 ' 0.015.' 0.009 0.015 '

0O12

0.009

4

4

_{.2 UA}

Fig.

4 Jj UI., .0 U0 u

Schematic streamline patterns generated by a diffuser and an actuator disk.

DIFFUSER

ACTUATOR

DEVICE FOR MEASURING FORCE ON THE DIFFUSER

R .AR2

PROPI)LS1ON TEST

DIFFUSER TEST

R . R1

Fig. 3. Bálänce of forces during apropulsion and a diffuser

Fig.. 4. Geörnetry öf diffusers.

DETAIL: LEADING EDGE. DIFFUSER.

Fig. 5. Axial velöcity distributions in nominal (CT.0)

- 0.0 C1 2.8 C1 8.0 170 leo 140 1501 130 120

itt

¿_

ut' tw

go

Ii

WAWJ

70 60

1

FIg.

Transverse velocity components in nominal (CT=0.0) and effective wake fields 4.9 and 6.0)

SEPARATION LINE

LIMITING STREAMLINES

Fig. 7.Bilge.vortex generation by three-dimensional f low

FORCE (kgf.1O') 60 40 FH E .1V TANKER

N RESULTS OF CALCULATIONS BASED ON NOMINAL WAKE

E RESULTS OF CALCULATIONS BASED ON EFFECTIVE WME

M RESULTS OF MEASUREMENTS 40 T F14 FV 0 MM N M MH E

Ii

MV D -FM FV

STATIC TRANSVERSE SHAFT FORCE ANO MOMENT

60 40 20 o

T:

LNG CARRIER MH

FIRST HARMONIC AMPLITUDES 0F THE THREE COMPONENTS 0F TI-lE FWCTUATING SHAFT FORCE AND MOMENT

Fig. 8. Comparison of calculated and measured components of shaft force and moment.

O MH MV 1 E E 20- I _20- I NI N

oj

IIM N1 I MOMENT (kgm.103) 100 eo N 60 40 N 20 EMM M EM O 100-MOMENT E FORCE N -(kgrn.lci') (kgf.103)